QUESTION BANK
Sub Code/Name: Fluid Mechanics & Machineries
UNIT- I PART-A
1. Define viscosity?2. What is compressibility?
3. Define dynamic viscosity?
4. What is cause for viscosity?
5. Give some example of surface tension ?
6. Define vapour pressure?
7. Define vapour pressure?
8. Give the Euler’s equation of motion?
9. What is bernouillie’s equation for real fluid?
10. State momentum equation and Impulse momentum equation?
11. State moment of momentukm equation?
12. State Bernouillie’s theorem?
13. Differentiate steady and unsteady flow?
14. State the assumptions in Bernoulli’s equation.
UNIT- I PART-B
1. a) Derives Euler’s Equation of Motion and proves the Bernoulli’s equation. (12 Marks)
b) Define the terms: i) Steady and unsteady flows ii) Specific weight (4 Marks)
2. a) Define the terms: i) Kinematics of flow ii) Uniform and non-uniform flows iii) Rotational and irrotational flows (6 Marks)
b) The Velocity Distribution for flow over a flat plate is given by u=(2/3)y-y2, Where u is the point velocity in metre per second at a distance y metre above the plate. Determine the shear stress aty=0 and y=15 cm. Assume dynamic viscosity as 8.63 poises (10Marks)
3. a) A pipe 200mm long has a slope of 1in100 and tapers from 1.2m diameter at the high end to 0.6m diameter at the low end and carries 100litres/sec of oil (Sp. Gr.=0.8). If the pressure gauge at the high end reads 60kN/m², determine i) Velocities at the two ends and ii) pressure at the lower end. (12 Marks)
b) One litre of crude oil weighs 9.6 N. Calculate its Specific weight and density (4 Marks)
4. Two large plane surfaces are 150mm apart. The space between the surfaces is filled with oil of viscosity 0.972Ns/m². A flat thin plate of o.5m² area moves through the oil at velocity of 0.3m/sec. Calculate the drgg force
i) When the plate is in the middle of the two plane surfaces and
ii)When the thinplate is at a distance of 30mm from one of the planes.(16 Marks)
5. a) Derive the three dimensional Continuity equation. (10 Marks)
b)Define the following i) Compressibility ii) Vapour pressure iii) Capillarity (6Marks)
6. a) Two plates are placed at a distance of 0.15mm apart. The lower plate is fixed while the upper plate having surface area 1.0 m2 is pulled at 0.3nm/s. Find the force and power required to maintain this speed, if the fluid separating them is having viscosity 1.5 poise. (8 Marks)
b) An oil film of thickness 1.5 mm is used for lubrication between a square plate of size 0.9m *0.9m and an inclined plane having an angle of inclination 200 . . The weight of square plate is 392.4 N and its slides down the plane with a uniform velocity of 0.2 m/s. find the dynamic viscosity of the oil. (8 Marks)
7. A pipe 300m long has a slope of 1 in100 and tapers from 1m diameter at the high end to 0.5m at the low end . The quantity of water flowing is 5400 m3/min. If the pressure at the high end is 49033 N/m², find the pressure at the low end. What is the change in pressure if the head loss between the two sections is 0.45m of water? (16 Marks)
8. 250 liters/sec of water is flowing in a pipe having a diameter of 300mm. If the pipe is bent by 135° (that is change from initial to final direction is 135°), find the magnitude and direction of the resultant force on the bend. The pressure of water flowing is 39.24N/cm². (16 Marks)
9. The diameter of a pipe gradually reduces from 1m to 0.7m. The pressure intensity at centerline of 1m section 7.848kN/m² and the rate of flow of water through the pipe is 600liters/sec. Find the intensity of pressure at the centerline of 0.7m section. Also determine the force exerted by flowing water on transition of the pipe. (16 Marks)
10.a) State the momentum equation. How will you apply momentum equation for determining the force exerted by a flowing fluid on a pipe bend? (12 Marks)
b) Define Moment of Momentum equation. Where this equation is used? (4 Marks)
UNIT- II PART-A
1. What do you mean by the term ‘Boundary Layer’?2. What is Laminar sub-layer?
3. Define Momentum thickness in Boundary Layer concept.
4. Sketch the development of Boundary layer over a flat plate.
5. Define the term ‘Turbulence’
6. Define: ‘Hydraulic Gradient Line’
7. Define: ‘Total gradient Line’
8. What is the expression for head loss due to friction in Darcy formula ?
9. What are the factors to the determined when viscous fluid flows through the circular pipe ?
10. What do you understand by the terms a) major energy losses , b) minor energy losses?
11. Give an expression for loss of head due to sudden enlargement of the pipe :-
12. Give an expression for loss of head due to an obstruction in pipe
13. What are the basic educations to solve the problems in flow through branched pipes?
UNIT- II PART-B
1. a) Define Displacement thickness. Derive an expression for the Displacement thickness. (10 Marks)b) Define: i) Laminar Boundary layer ii) Laminar Sub-layer (6 Marks)
2. a) A thin plate is moving in still atmospheric air at a velocity of 5m/sec. The length of the plate is 0.6m and width 0.5m. Calculate i) the thickness of the boundary layer at the end of the plate and ii) Drag force on one side of the plate. Take density of air as 1.24 kg/m3 and kinematic viscosity 0.15 strokes. (10 Marks)
b) What do you understand by the term Boundary layer and Boundary Layer theory? (6 Marks)
3. a) A plate of 600mm length and 400mm wide is immersed in a fluid of specific gravity 0.9
and kinematic viscosity 10-4 m²/sec. The fluid is moving with a velocity of 6 m/sec. Determine i) boundary layer thickness ii) shear stress at the end of the plate, and iii) drag force on one side of the plate. (12 Marks)
b) Differentiate Laminar & Turbulent Flow. (4 Marks)
4. a) What do you understand by the terms: Major energy losses and Minor energy losses (8 Marks)
b) Obtain expression for head loss in a sudden expansion in the pipe. List all the assumptions
made in the derivation. (8 Marks)
5. a) Derive the darcy-Weishach equation. (10 Marks)
b) Water is flowing through a pipe of diameter 250mm with a velocity of 3m/sec. Find the head loss due to friction for a length of 5.5m, if the coefficient of friction f is given by f = [0.03 (0.08/Re0.3)] where kinematic viscosity = 0.01strokes. (6 Marks)
6. The difference in water level between two tanks which are connected by three pipes in series is 15m. Lengths and diameters of these pipe are 300m, 150m, 200m and 30cm, 20cm, and 30cm respectively. Find the discharge through the pipe line and tabulate all losses if friction factor for three pipes are taken as 0.02, 0.025 and 0.03 (16 Marks)
7. a) A sudden enlargement of a water main from 230mm to 460mm diameter, the hydraulic gradient rises by 10mm. Estimate the discharge. (10 Marks)
b) Obtain expression for head loss in a sudden contraction in the pipe. (6 Marks)
8. Determine the length of an equivalent pipe of diameter 20cm and friction factor is 0.02 for a given pipe system discharging 0.1 m3/sec. The pipe system consists of the following. i) 10m line of 20cm diameter with friction factor 0.03, ii) three 90° bend with k=0.5 for each, iii) two sudden expansion of diameter 20cm to 30cm , iv) a 15cm line of 30cm diameter with friction factor is 0.025 and v) a global valve fully open with k=10. (16 Marks)
9. Two reservoirs whose water surface elevations differ by 40m are connected by a pipe line 30cm in diameter and 3km long. In order to increase the discharge, an additional pipe line 20cm in diameter and 1.5km long is laid parallel from the mid point of the first one upto the lower reservoir. What is the increase in discharge due to newly laid pipe? Assume friction factor f = 0.02 (16 Marks).
UNIT- III PART-A
1. Define Dimensional Analysis2. Define dimensionally homogeneous equation.
3. What are the methods of dimensional analysis?
4. State Buckingham’s Π theorem
5. What is dimensionless number?
6. What are the condition for hydraulic similitude?
7. Explain the significance of Froude Model law
8. Explain the terms: Model and Prototype
9. List advantages of Dimensional Analysis.
10. Explain Model analysis.
UNIT- III PART-B
1. a) Explain with example, dimensional homogeneity of a physical equatyion. (6 Marks)b) Describe in detail the method of dimensional analysis using Buckingham’s π theorem. (10 Marks)
2. a) Define i) Geometric similarity ii) Dynamic similarity iii) Kinematic similarity. (6 Marks)
b) The efficiency of a fan η depends upon following factors : 1) Density ρ 2) Dynamic viscosity μ 3) Diameter D 4) Discharge Q and 5) Angular velocity ω, Show that η = Φ [μ/D²ωρ , Q/D3ω ]. (10 Marks)
3. The pressure difference ΔP in a pipe of diameter D and length L due to turbulence flow depends on the velocity V, viscosity μ, density ρ and roughness K. Using Buckingham’s π theorem, obtain an expression for ΔP. (16 Marks)
4. The discharge Q through an oil ring depends on the diameter D of oil ring, speed Nrpm, mass density ρ of oil, absolute viscosity μ of oil, surface tension σ and specific weight ע of oil. Show that Q = ND3 f [ μ / ρND² , σ / ρN²D3 , ע / ρN²D ] (16 Marks)
5. Power P developed by a water turbine depends upon rotational speed N, operational head H, diameter D, breath B of runner, density ρ, viscosity μ and gravity g show that P = ρD5N5 Φ[H/D, B/D, ρD²N/μ, ND/(gH)1/2 ] (16 Marks)
6. Torque T of a propeller depends upon density of liquid ρ, viscosity μ, speed N, linear velocity V, diameter of the propeller shaft D. Using Buckingham’s π theorem show that T= ρN²D5 f[ ND/V, ρND²/μ ] (16 Marks)
7. a) A pipe of diameter 1.5m is required to transport an oil of specific gravity 0.9 and viscosity 3X10-2poise at the rate of 3000lit/sec. Tests were conducted on a 15cm diameter pipe using water at 20°C. Find the velocity and rate of flow in the model. Viscosity of water at 20°C is 0.01poise. (8 Marks)
b) The ratio of length of a sub-marine and its model is 30:1. The speed of the sub-marine (prototype) is 10m/sec. The model is to be tested in a wind tunnel. Find the speed of air in wind tunnel. Also determine the ratio of drag (resistance) between the model and prototype. Take the value of kinematic viscosity for sea water and air as 0.012strokes and 0.016strokes respectively. The density for sea water and air is given as 1030kg/m3 and 1.24kg/m3 respectively. (8 Marks)
8. a) The pressure drop in an aero-plane model of size 1:40 of its prototype is 80N/cm². The model is tested in water. Find the corresponding pressure drop in the prototype. Take density of air 1.24 kg.m3. The viscosity of water is 0.01poise while the viscosity of air is 0.00018poise. (10 Marks)
b) Derive Euler, Froude and Weber numbers. (6 Marks)
UNIT- IV PART-A
1. What is a hydraulic turbine?2. How will you classify the turbine?
3. Differentiate between the reaction and impulse turbine
4. Define specific speed of turbine
5. Give example for a low head, medium head and high head turbine.
6. What is Draft tube?
7. What is cavitation? How can it be avoided in reaction turbine?
8. Define the term ‘Governing of a turbine’
9. What are the functions of Surge tank?
10. Differentiate between an inward and an outward flow reaction turbines.
11. List out advantages of Francis turbine
12. Mention main components of Centrifugal pump
UNIT- IV PART-B
1. A jet of water having velocity of 20m/sec strikes a curved vane, whish is moving with a velocity of 10m/sec. The jet makes an angle of 20° with the direction of motion of vane at inlet and leaves an angle of 130° to the direction of motion of vane at outlet. Calculate i) Vane angles, so that the water enters and leaves the vane without shock. ii) work done per second per unit weight of water striking the vane per second. (16 Marks)2. A jet of water having velocity of 15m/sec strikes a curved vane which is moving with a velocity of 5m/sec. The vane is symmetrical and it so shaped that the jet is deflected through 120°. Find the angle of the jet at inlet of vane so that there is no shock. What is the absolute velocity of jet at outlet in magnitude and direction and the work done per unit weight of water. Assume the vane to be smooth. (16 Marks)
3. A jet of water having velocity of 30m/sec strikes a series of radial curved vanes mounted on a wheel which is rotating at 200rpm. The jet makes an angle of 20° with the tangent to the wheel at inlet and leaves the wheel with a velocity of 5m/sec at an angle of 130° to the tangent to the wheel at outlet. Water is flowing from outward in a radial direction. The outer and inner radii of the wheel are 0.5m and 0.25m respectively. Determine i) Vane angles at inlet and outlet ii) work done per unit weight of water iii)efficiency of wheel. (16 Marks)
4. The penstock supplies water from a reservoir to the pelton wheel with a gross head of 500m. One third of the gross head is lost in friction in the penstock. The rate of flow of water through the nozzle fitted at the end of the penstock is 2m3/sec. The angle of deflection of the jet is 165°. Determine the power given by the water to the runner and hydraulic efficiency of the pelton wheel. Take speed ratio=0.45 and Cv=1 (16 Marks)
5. A pelton wheel having a mean bucket diameter of 1m and is running at 1000rpm. The net head on the pelton wheel is 700m. If the side clearance angle is 15° and discharge through nozzle is 0.1m3/sec. Find i) Power available at the nozzle ii) Hydraulic efficiency of the turbine. (16 Marks)
6. A reaction turbine works at 450rpm under a head of 120m. Its diameter at inlet is 120cm and the flow area is 0.4m². The angle made by absolute and relative velocities at inlet are 20° and 60° respectively with the tangential velocity. Determine i) The volume flow rate ii) The power developed iii) Hydraulic efficiency (16 Marks)
7. As inward flow reaction turbine has external and internal diameters as 1m and 0.6m respectively. The hydraulic efficiency of the turbine is 90% when the head on the turbine is 36m. The velocity of flow at outlet is 2.5m/s and discharge at outlet is radial. If the vane angle at outlet is 15° and width of the wheel is 100mm at inlet and outlet, Determine i) the guide blade angle ii) speed of the turbine iii) vane angle of the runner at inlet iv) volume flow rate of turbine v) power developed. (16 Marks)
8. A Pelton turbine is required to develop 9000kW when working under a head of 300m the impeller may rotate at 500rpm. Assuming a jet ratio of 10 and an overall efficiency of 85%. Calculate i) quantity of water required ii) diameter of wheel iii) Number of jets iv) Number and size. of bucket on the runner. (16 Marks)
9. The following data is given for a Francis turbine. Net head = 80m, Speed = 700rpm, Shaft power = 300kW, Overall efficiency = 80%, Hydraulic efficiency = 90%, flow ratio =0.2, and breadth ratio = 1. The thickness of vane occupies 4% of circumferential area of the runner, velocity of flow is constant at inlet and outlet and discharge is radial at outlet. Determine i) Diameters of runner at inlet and outlet, assume D2=D1/2. ii) Width of wheel at inlet iii) Guide blade angles iv) runner vane angles at inlet and outlet. (16 Marks)
10. i) Draw a neat sketch of Kaplan turbine, name the parts and briefly explain the working. (8 Marks)
ii) Define specific speed of the turbine? Derive an expression for the specific speed. (8 Marks)
UNIT- V PART-A
1. What is meant by Pump?2. What is meant by Priming?
3. Differentiate between the single acting pump and double acting pump
4. What are the functions of air vessels?
5. Define slip, percentage slip and negative slip of a reciprocating pump
6. Define Manometric efficiency
7. Define Mechanical efficiency.
8. Define overall efficiency.
9. Define speed ratio, flow ratio.
10. Mention main components of Reciprocating pump.
11. What is indicator diagram?
12. What is meant by Cavitations?
UNIT- V PART-B
1. A radial flow impeller has a diameter 25cm and width 7.5cm at exit. It delivers 120litres of water per second against a head of 24m at 1440rpm. Assuming the vanes block the flow area by 5% and hydraulic efficiency of 80%. Estimate the vane angle at exit. Also calculate the torque exerted on the driving shaft if the mechanical efficiency is 95%. (16 Marks)2. Find the power required to drive a centrifugal pump which delivers 0.04m3/sec of water to a height of 20m through a 15cm diameter pipe and 100m long. The overall efficiency of the pump is 70% and coefficient of friction is 0.15 in the formula Hf= 4flv2 / 2gd. (16 Marks)
3. A centrifugal pump having outer diameter equal to 2 times the inner diameter and running at 1200rpm works against a total head of 75m. The velocity of the flow through the impeller is constant and equal to 3m/sec. the vanes are set back at an angle of 30° at outlet. If the outer diameter of the impeller is 600mm and width at outlet is 50mm. Determine i) Vane angle at inlet ii) Work done per sec by the impeller iii) Manometric efficiency. (16 Marks)
4. The impeller of a centrifugal pump has an external diameter of 450mm and internal diameter of 200mm and it runs at 1440rpm. Assuming a constant radial flow through the impeller at 2.5m/sec. and that the vanes at exit are set back at an angle of 25°. Determine i)Inlet vane angle ii) The angle, absolute velocity of water at exit makes with the tangent and iii) The work done
per N of water. (16 Marks)
5. The diameter and stroke of a single acting reciprocating pump are 200mm and 400mm respectively, the pump runs at 60rpm and lifts 12litres of water per second through a height of 25m. The delivery pipe is 20m long and 150mm in diameter. Find i) Theoretical power required to run the pump ii) Percentage of slip iii) Acceleration head at the beginning and middle of the delivery stroke. (16 Marks)
6. The length and diameter of a suction pipe of a single acting reciprocating pump are 5m and 10cm respectively. The pump has a plunger of diameter 150mm and stroke of length of 300mm. The centre of the pump is 4m above water surface in the pump. The atmospheric pressure head is 10.3m of water and pump is running at 40rpm. (16 Marks)
7. Two geometrical similar pumps are running at the speed of 750rpm. One pump has an impeller diameter of 0.25m and lifts the water at the rate of 30 lit/sec against a head of 20m. Determine the head and impeller diameter of the other pump to deliver half the discharge. (16 Marks)
8. i) What is reciprocating pump? Describe the principle and working of a double acting reciprocating pump with a neat sketch. (12 Marks)
ii) Define slip, percentage slip and negative slip of a reciprocating pump. (4 Marks)
9. A double acting reciprocating pump running at 60rpm is discharging 1.5m3 of water per minute. The pump has a stroke length of 400mm. The diameter of the piston is 250mm. The delivery and suction heads are 20m and 5m respectively. Find the power required to drive the pump and the slip of the pump. (16 Marks)
10. A double acting reciprocating pump has a bore of 15cm diameter and stroke 30cm long. The piston rod diameter is 25mm. The crank rotation speed is 60rpm. The water is lifted to a height
of 20m and the percentage of slip is -2 (negative value). Find the actual discharge of the pump
and the power required to lift the water. (16 Marks)
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